Question

simplify cube root -108 a to the power 4 b cube in the simplest form

Answer 1

Given:

cube root -108 a to the power 4 b cube

To find:

Simplify cube root -108 a to the power 4 b cube in the simplest form

Solution:

From given, we have an equation,

cube root -108 a to the power 4 b cube

cube root of a negative number is a negative number.

∴ cube root -108 a to the power 4 b cube =

- cube root 108 a to the power 4 b cube

cube root of (b cube) = b

cube root of (a to the power 4) = $\sqrt[3]{a^4}= \sqrt[3]{a^3 \times a}= a\sqrt[3]{a}$

cube root of  108 = $\sqrt[3]{108} = 3\sqrt[3]{4}$

∴ cube root -108 a to the power 4 b cube = -3∛4a∛ab

In equation form:

$\sqrt[3]{-108a^4b^3} = -\sqrt[3]{108a^4b^3}=-3\sqrt[3]{4}\sqrt[3]{a^4}\sqrt[3]{b^3}=-3\sqrt[3]{4}a\sqrt[3]{a}b$